How do you convert 4/7 into a decimal?

1 Answer
George C.
Oct 3, 2017

#4/7 = 0.571428571428... = 0.bar(571428)#

Explanation:

Long divide until the remainder repeats. Then the quotient will repeat from that point on.

#color(white)(00")")underline(color(white)(0)0color(black)(.)5color(white)(.)7color(white)(.)1color(white)(.)4color(white)(.)2color(white)(.)8color(white)(.))#
#7color(white)(0)")"color(white)(0)4color(black)(.)0color(white)(.)0color(white)(.)0color(white)(.)0color(white)(.)0color(white)(.)0color(white)(.)#
#color(white)(00")"0)underline(3color(white)(.)5)#
#color(white)(00")"00.)5color(white)(.)0#
#color(white)(00")"00.)underline(4color(white)(.)9)#
#color(white)(00")"00.)color(white)(0.)1color(white)(.)0#
#color(white)(00")"00.)color(white)(0.)underline(color(white)(0.)7)#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)3color(white)(.)0#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)underline(2color(white)(.)8)#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)color(white)(0.)2color(white)(.)0#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)color(white)(0.)underline(1color(white)(.)4)#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)color(white)(0.)color(white)(0.)6color(white)(.)0#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)color(white)(0.)color(white)(0.)underline(5color(white)(.)6)#
#color(white)(00")"00.)color(white)(0.)color(white)(0.)color(white)(0.)color(white)(0.)color(white)(0.)4#

In this example, we see that the remainder #4# repeats, so the quotient repeats too and we find:

#4/7 = 0.571428571428... = 0.bar(571428)#

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